What it means
- Conditional probability is the probability of an event, given that another event has already happened.
- When you know that B has happened, you only look at the outcomes in B. The total you divide by changes.
From tables and Venn diagrams
- P(A given B) = number in both A and B ÷ number in B.
- 40 people wear glasses, and 15 of them are left-handed. Given that a person wears glasses, P(left-handed) = 15/40 = 3/8.
From tree diagrams
- On a 'without replacement' tree, the second set of branches is conditional: it depends on what happened first.
- With 3 red and 2 blue counters, P(second is red given the first was red) = 2/4 = ½.
The formula
- P(A given B) = P(A and B) ÷ P(B). If P(A and B) = 0.12 and P(B) = 0.4, then P(A given B) = 0.3.
- If A and B are independent, P(A given B) = P(A): knowing B makes no difference.
Key terms
- Conditional probability
- The probability of an event, given that another event has happened.
- Given
- Already known to have happened.
- Independent
- When one event does not change the probability of the other.
- P(A and B)
- The probability that both A and B happen.